Previously we saw that quantum GR, based on the Einstein-Hilbert
action, is a non-renormalizable theory. On the other hand, by adding
the general fourth-derivative terms, we arrive at the model providing
multiplicative renormalizability. Another strong argument for
including fourth-derivative terms is that they are required for the
renormalizability of the semiclassical theory, when gravity is an
external field [1]}, [2]}, [3]}, [4]}. And this is something
one cannot disregard. The point is that the concepts of QFT from one
side and of the curved space from another, are well-established and,
to a great extent, verified by experiments and observations. Thus, if
QFT in curved space produces the four-derivative terms in the action,
we have to admit that these terms are there. The problem concerns
not exactly UV divergences and formal renormalizability. Together
with the logarithmic divergences there are always logarithmic
nonlocal form factors. In the IR such a form factor behaves,
effectively, as a constant [5]}, [4]}. This means, if we do
not include fourth derivatives into the action, they will come there
anyway as legitimate corrections coming from quantum matter fields.
Therefore, independent on which approach to QG we choose, it makes
sense to include fourth derivatives terms into the gravitational
action and check out the physical consequences of this inclusion.
